In this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging (MCIL) tool in deviated and layered anisotropic formations through a numerical mode matching method (NMM). First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle θ so that the electromagnetic (EM) fields produced by the dipoles can be transformed into three axisymmetric problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. The numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.

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In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR). INDEX TERMS Directional antennas, receiving antennas, electromagnetic propagation in absorbing media, geophysical measurement techniques, well logging.

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The azimuth electromagnetic wave resistivity while drilling is a new type of well logging technique. It can real-time detect the formation boundary, realize geosteering and borehole imaging in order to keep the tool always drilling in the some meaning reservoir. For effectively optimizing tool parameters, proper explanation and evaluation of the data obtained by azimuth electromagnetic wave resistivity while drilling, the efficient numerical simulation algorithm is required. In this paper, we use the finite volume algorithm in the cylindrical coordinate to establish the corresponding numerical method so that we can effectively simulate the response of the tool in various complex environments and investigate the influences of the change in formation and tool parameters on the tool response. Therefore, according to the typical coil architecture of the instrument of azimuth electromagnetic wave resistivity while drilling, we first introduce the electrical and magnetic dyadic Green's functions in inhomogeneous anisotropic formation by the electrical current source in the cylindrical coordinate. Through superposition principle, we derive the integral formula to compute the electric field intensity excited by tilted transmitter coils and the induction electrical potential on tilted receiving coils both mounded on the drill collar. Then, we use the coupled electrical potentials of the dyadic Green's functions to overcome the low induction number problem during modeling the electrical fields in inhomogeneous anisotropic formation. Furthermore, we use Lebedev grid in both and z directions to reduce the number of grid nodes, and the standard method to compute the equivalent conductivity in heterogeneous units for enhancing the discrete precision. On the basis, by the three-dimensional finite volume method, we discrete the equations about the coupled electrical potentials in the cylindrical coordinates and obtain the large sparse algebraic equation sets about the coupled electrical potentials field on the Lebedev grid. A combination of incomplete LU decomposition with the bi-conjugate gradient stabilization is used to solve the numerical solution. Finally, we validate the algorithm by comparing the numerical results obtained by two different methods, study the effects of the drill collar, anisotropy, the tilted angles of both coil, and borehole on the instrument response in inhomogeneous anisotropic formation. The numerical results show that the tool response obtained by the three-dimensional finite volume algorithm in the cylindrical coordinate system in anisotropic formation accord with that those obtained by other algorithms. The drill collar, inhomogeneous anisotropic n the formation will lead to both the smaller amplitude ratio and the smaller phase difference. In addition, when the coils of both transmitting and receiving coils are tilted, the amplitude ratio and phase difference of the tool are more sensitive to the change in formation parameter.

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Positronium (Ps) formation for positron impact on metastable hydrogen in 2s state has been studied by using the twochannel, two-center eikonal final state-continuum initial distorted wave (EFS-CDW) method. The differential, integrated, and total cross sections for Ps formation in different states have been calculated from each channel opening thresholds to high energy region. The results are compared with other theoretical calculations available in the literature. For Ps formation in s-state at intermediate and high energies, our results are in good agreement with the prediction of distorted wave theory. Those formed in p-states and the total Ps formation cross sections are reported for the first time. It is shown that the total Ps formation cross sections for positron scattering from H(2s) state are significantly larger at relatively low energies, while smaller at high energies, compared with those obtained from hydrogen in ground state.

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